Sensors are often used to measure a motion of an object. For example, vibratory meters typically use sensors to measure the position, velocity, or acceleration of a tube. In particular, the vibratory meter can use a driver to vibrate the tube filled with material such as a fluid. The sensors can measure a movement of the tube to determine properties of the fluid in the tube. Motions of other objects can also be measured. For example, vibrations of a frame in a building or automobile, the sway of a rocker arm in a linkage system, or the like, can also be measured by the sensors. The motions of these objects can be sinusoidal. For example, the vibration of a tube can approximate one or more sinusoidal motions. The sinusoidal motion is typically described in terms of kinematic properties, such as the magnitude and frequency of the motion. The kinematic property can include the displacement, velocity, and acceleration of the motion.
A parameter of the signal, such as a voltage or current, provided by the sensor may be proportional to the kinematic property of the motion. For example, when velocity sensors are employed, the magnitude of the voltage can be correlated with the velocity of the sensor. As can be appreciated, other sensors can measure the displacement and acceleration of the objects. For example, displacement sensors can measure the displacement of an object away from a reference location. An accelerometer can measure the acceleration of the object. The sensors measuring these and other kinematic properties can provide a signal, which may be sinusoidal, comprised of sinusoidal components, or the like.
The signal can be digitized so digital signal processing can be performed to calculate the properties of the object or other properties, such as properties of the fluid in the vibrating meter's flow tube. Digitizing the signal can be comprised of sampling and encoding the signals. The samplings are typically voltage measurements that are performed at specific times, which may be periodic. In periodic sampling, the number of samples per unit time is commonly referred to as a sampling rate. The sampling rate is typically represented as fs=1/T, where T is the time-period between each sampling. Each sampling can be encoded with a byte representation that corresponds to the voltage of the sampling. The number of bits available for each encoding is known as the bit resolution. The sampling and encoding is typically done with an analog-to-digital converter (ADC).
As a result of the bit resolution, samples with different voltage values often have the same byte representation. For example, a sampling of 1.2 volts and a sampling of 1.01 volts may have the same byte representation. Digitizing the signal can therefore introduce an error in the digital signal. The error introduced during digitization is sometimes referred to as the quantization error. There are various methods to reduce or eliminate the error. These methods might include increasing the bit resolution, implementing companding algorithms, etc. However, such methods can consume limited processing resources and increase the cost and complexity of the electronics that perform the processing.
Accordingly, there is a need for a method and an apparatus for reducing the error rate. There is also a need to reduce the error rate while not consuming limited processing resources and without significantly increasing the cost and complexity of the meter electronics.